h-Cobordism Theorem

The -cobordism theorem states that if is a simply connected, compact manifold with a boundary that has two components, and , such that inclusion of each is a homotopy equivalence, then is diffeomorphic to the product for . In other words, if and are two simply connected manifolds of dimension and there exists an h-cobordism between them, then is a product and is diffeomorphic to .

The proof of the -cobordism theorem can be accomplished using surgery. A particular case of the -cobordism theorem is the Poincaré conjecture in dimension . Smale proved this theorem in 1961.